Uniqueness theorems for the Dirac operator with eigenparameter boundary conditions and transmission conditions

ABSTRACT

Inverse spectral problems are considered for the Dirac operator with boundary conditions depending polynomially on the spectral parameter and with a finite number of transmission conditions. We investigate two inverse problems of recovering the operator either from the so-called Weyl function or from two spectra. Furthermore, we also extend Hochstadt–Lieberman theorem to our cases.

KEYWORDS:

• Dirac operator
• eigenparameter-dependent boundary conditions
• transmission conditions
• uniqueness theorem

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 34A55
• 34L40
• 34L05

Acknowledgements

The authors would like to thank the referees for careful reading of the manuscript and helping us to improve the presentation by providing valuable and insightful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research was supported in part by the National Natural Science Foundation of China (11601299, 11571212, 11471004), and the Fundamental Research Funds for the Central Universities (GK201701001).